April 27th, 2018, 02:03 AM  #1 
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1  limit of arctan(x/m)
please check the given limit is correct or not. as the value of arctanx or tan inverse x cannot exceed π/2, but its limit written here is π for m<O.

April 27th, 2018, 02:08 AM  #2 
Senior Member Joined: Oct 2009 Posts: 555 Thanks: 179 
You are right, it doesn't make any sense.

April 27th, 2018, 03:33 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra 
It depends on the definition of $\arctan x$. If we define $$\frac\pi2 < \arctan x < \frac\pi2$$ then you are correct, but if we define $$0 < \arctan x < \pi$$ then the book is correct. 
April 27th, 2018, 06:22 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
Does the book allow $s$ to be negative?

April 27th, 2018, 10:52 PM  #5  
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1  Quote:
will arctanx remain a function? it will have three values for one x. Help me if I am wrong.  
April 27th, 2018, 10:56 PM  #6  
Newbie Joined: Apr 2017 From: Bhadohi, U.P., India Posts: 26 Thanks: 1  Quote:
 
April 27th, 2018, 11:01 PM  #7 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,445 Thanks: 2499 Math Focus: Mainly analysis and algebra  
April 27th, 2018, 11:18 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
If $s$ isn't real, "greater than zero" doesn't make sense. If $s$ is real and positive, the original question is effectively about a onesided limit. It's possible for arctan(0) to be defined as $\pi$ (or some other multiple of $\pi$), but it's usually defined as 0. The situation with the arccot function is rather different... it's much easier to find differences of opinion about arccot(0). 

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